Incoherent X-Ray Scattering by a Statistical Atom

Abstract

The theory of the homogeneous interacting electron gas is used to derive a functional of the density for the form factor for incoherent scattering of x rays by a statistical atom. The results show a dramatic improvement over an early calculation of Heisenberg who used the Thomas-Fermi model. Detailed calculations of form factors are carried out for several elements (A, Cu, Ce, Na) and compared with the results of Hartree-Fock-Slater (HFS) self-consistent wave-function calculations. Whereas the Thomas-Fermi model gives incoherent cross sections which differ at low energies by orders of magnitude from those given by the HFS model, the theory of the homogeneous electron gas yields results which compare within 15% of the HFS results.